Question

Justify statement 1-4 and explain why.

If a matrix A is invertible, then all the eigenvalues of A are nonzero. If two linear maps have the same characteristic polynomial, then they always have the same Jordan canonical form. If a linear map from the vector space P of all polynomials to itself is injective, then it is an isomorphism. If W, and W2 are subspaces of a vector space V, then the projection T: W W 2 → W, i.e., T(x + y) = r. Var EW, Vy E W2, is linear aud T2 =T.

Answer 1

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